Nonlinear dynamics of interacting population in a marine ecosystem with a delay effect

In this paper, we propose a new tritrophic food chain model. We address the conditions for the coexistence of two different zooplankton species and one phytoplankton species. The results of the numerical and analytical studies of the model show that the most relevant parameters influencing the plankton ecosystem, to maintain a stable coexistence equilibrium, are the: carrying capacity and the constant intrinsic growth rate of the phytoplankton population, and the conversion rate with a mortality rate of carnivorous zooplankton. We prove the existence and direction of Hopf bifurcation in non delay system. To account for the time delay in the conversion of herbivorous consumption to carnivorous zooplankton, we incorporate a discrete delay into the consume response function. Furthermore, we establish some adequate conditions to prove the occurrence of Hopf bifurcation induced by delay in the delayed model. We also plot two-parameter bifurcation diagrams. The numerical results support the analytical findings.